SOLUTION: What is each of the five children's ages, if they are each born a year apart AND the product of their ages is 6,720?

Question 772586: What is each of the five children's ages, if they are each born a year apart AND the product of their ages is 6,720?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The ages will be either
A) 3 consecutive odd numbers along with the 2 even numbers in between,
or
B) 3 consecutive even numbers and the two odd numbers in between.

The prime factorization of 6,720 is

We cannot regroup the prime factors into 5 factor as described in A) above, because alonng with 3, 5, and 7, we would need 6, and that would require an extra 3 as a prime factor.
WE must use 5 and 7 as our ofdd numbers and that means 4,6,and 8, as our even numbers.
is the product needed.
The children's ages are 4, 5, 6, 7, and 8.

We could have said
= age of the middle child, so
= age of the youngest child,
= age of the second youngest child,
and being the ages of the two oldest ones.
Then the product would be

We could write as an equation, but that is not very helpful.
At most we could have said
,
and knowing that would have suggested .
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